Conventional epitaxial techniques requires single crystalline substrates to form semiconductor material of desired material quality for device applications. The use of amorphous substrates, in many applications, provides an opportunity to consider new materials and designs, which can fundamentally alter the performance, functionality and/or cost limitations of many optoelectronic devices. Here, a growth process is described to achieve single crystalline GaN material on amorphous SiO2. The evolutionary selection principle in crystal growth is the basis of this technique, and the mechanism is described and analyzed in detail. It is expected that this process can be extended to other semiconductor and substrate combinations, allowing heterogenous integration with functional substrates to produce new classes of semiconductor devices.